The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function

@article{Berg2007TheFP,
  title={The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function},
  author={Christian Berg and Antonio J. Dur'an},
  journal={Mathematica Scandinavica},
  year={2007},
  volume={103},
  pages={11-39}
}
We study the fixed point for a non-linear transformation in the set of Hausdorffmoment sequences, defined by the formula: T ((an))n = 1/(a0+�E �E �E+an).We determine the corresponding measure�E, which has an increasing and convex density on ]0, 1[, and we study some analytic functions related to it. TheMellin transform F of �E extends to ameromorphic function in the whole complex plane. It can be characterized in analogy with the Gamma function as the unique log-convex function on ].1… 

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